1 - Demonstrate the behavior you want - when a thread gets hijacked, reclaim it - start a separate thread with a clear subject line. Include the question from the PM and your response. Open the mail with an intro saying something non-accusatory, saying you started this separate thread as this is a separate issue, and you need to keep the first thread clear so you can continue with the original problem. Politely ask that everyone stay on the new thread for the issue.
2 - Recognize variance in formality - It sounds like you have 2 groups with 4 people - you, your PM, your peer, your peer's PM. So you and your PM are from one group, and your peer and her PM are the other. Different group dynamics will necessitate different levels of formality. In some cases, I've been able to start a quick informal mail for this sort of stuff, since it has been a case where everyone is pretty comfortable with each other and the two groups had been harmonious for quite some time. In other, tenser situations, I've had to tred more lightly and provide out of band communcation to either each person, or each group to get the same thing done, just so that no one lost face in front of anyone else.
3 - In a really tense situation - My order of operations would be:
The peer - "Hey, do you see this issue too? Is it impacting you the same way?" and then develop a plan for it. If your peer isn't convinced this is an issue, then raising it with the peer's PM could go badly. If she is in the same boat, then maybe she'd like to talk to her PM while you talk to yours.
Your PM - whether or not your peer agrees, a private conversation with your PM is in order - asking for his help fixing muddy threads and asking for his take on how questions could be asked without thread interruption is a great approach. Assuming you get him on board, the two of you may then strategize about how to engage the other side. It's possible that if your peer isn't on board, your PM may be willing to tackle the other PM, depending on the nature of the relationship.
Lastly- the external PM. I don't mean to leave the poor guy out of the loop, but if you have a tense situation, this is the person with the farthest political distance from you. You and your PM and you and your peer have relationships built on shared goals or shared work, the external PM doesn't have the same tie to you. In an easy going situation, this would be no big deal, a group mail saying "hey we have a problem" would be totally fine, but in a tense situation, you may want to be aware that this guy will do better hearing it from either a peer (your PM) or someone in his own organization.
4 - Tense?? I'm using a vague word here and wanted to clarify. I've been in situations where there is either a contractual or organizatoinal reason for two groups to be at odds, or where groups that would otherwise be harmonious have had such rocky progress that they no longer trust each other. At that point, a lack of care in terms of communication can make a bad situation worse, while careful communication can rebuild trust. I can't really define tension any better, because every situation is unique.